leetcode: 64. Minimum Path Sum

Q

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Example 1:

[[1,3,1], [1,5,1], [4,2,1]]

Given the above grid map, return 7. Because the path 1→3→1→1→1 minimizes the sum.

AC

class Solution(object):    def minPathSum(self, grid):        """        :type grid: List[List[int]]        :rtype: int        """        sum = list(grid[0])        for j in xrange(1, len(grid[0])):            sum[j] = sum[j - 1] + grid[0][j]        for i in xrange(1, len(grid)):            sum[0] += grid[i][0]            for j in xrange(1, len(grid[0])):                sum[j] = min(sum[j - 1], sum[j]) + grid[i][j]        return sum[-1]# Time:  O(m * n)# Space: O(m + n)class Solution2(object):    def minPathSum(self, grid):        sum = list(grid[0])        for j in xrange(1, len(grid[0])):            sum[j] = sum[j - 1] + grid[0][j]        for i in xrange(1, len(grid)):            sum[0] += grid[i][0]            for j in xrange(1, len(grid[0])):                sum[j] = min(sum[j - 1], sum[j]) + grid[i][j]        return sum[-1]if __name__ == "__main__":    assert Solution().minPathSum([[0,1] ,[1,0]]) == 1    assert Solution().minPathSum([[1,3,1], [1,5,1], [4,2,1]]) == 7

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